Problem: Rewrite as a simplified fraction. ${0.7\overline{61} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 761.6161...\\ 10x &= 7.6161...\end{align*}}$ Subtracting the two equations, we have: ${990x = 754}$ ${x = \dfrac{754}{990}} $ ${x = \dfrac{377}{495}} $